two-body problem

The two-body problem is the problem of finding the positions and velocities of two massive bodies
that attract each other gravitationally, given their masses, positions,
and velocities at some initial time. It was first solved by Isaac Newton,
who showed mathematically that the orbit of one body about another was either
an ellipse, a parabola, or a hyperbola (see conic
sections), and that the center of mass of the system moved with constant
velocity.